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Proof step 128 from proof inv-rename-overwrite-reparent (previous step)

1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[inodekey(ino)]] = inodenode(key0, md1, true, m9, m12, m13), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m8), fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key3, m8), links(m8, fs0, ri0) = ∅ ++ dentrykey(ino, str1), fo.inodes?, ro.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(fi), ri-inj(ri0), ubifs-cons(fs0, ri0, ro, fi, fo, log0), ri0[inodekey(ino)] ∈ fs0, dentrykey(m, str) ∈ ri0, inodekey(m8) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m) ∈ ri0, inodekey(ino) ∈ ri0, ri0[dentrykey(ino, str1)] ∈ fs0, ri0[inodekey(m)] ∈ fs0, dentrykey(ino, str1) ∈ ri0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, ¬ fs0[ri0[inodekey(m8)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size, m10 ≠ 0 ∨ m = ROOT_INO, m9 ≠ 0 ∨ ino = ROOT_INO, ¬ fs0[ri0[inodekey(m8)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m8)]].size ⊦ adr1 = adr5, adr1 = adr4, adr1 = adr3, adr1 = adr2, adr2 = adr5, adr2 = adr4, adr2 = adr3, adr3 = adr5, adr3 = adr4, adr4 = adr5, dentrykey(m, str) = dentrykey(ino, str1), ino = 0, ino = m, m = 0, m8 = 0, m8 = ROOT_INO, inodekey(m8) ∈ ro, adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(ino, str1), adr2][inodekey(m), adr3][inodekey(ino), adr4], adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(ino, str1), adr2], inodekey(ino) ∈ ro, inodekey(m) ∈ ro, adr1 ∈ fs0, adr2 ∈ fs0, adr3 ∈ fs0, adr4 ∈ fs0, adr5 ∈ fs0, adr2 ∈ ri0 -- dentrykey(m, str), adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(ino, str1), adr2][inodekey(m), adr3]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 129:
⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0)
Proof step 130:
1 = fs0[ri0[inodekey(m8)]].nlink, fs0[ri0[dentrykey(ino, str1)]] = dentrynode(key3, m8), fs0[ri0[dentrykey(m, str)]] = dentrynode(key1, m8), fs0[ri0[inodekey(ino)]] = inodenode(key0, md1, true, m9, m12, m13), ro.inodes?, fo.inodes?, file-node-cons(fs0, ri0), log-cons(log0, fs0), replay-cons-strong(fs0, ri0, ro, fi, fo, log0), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), ubifs-cons(fs0, ri0, ro, fi, fo, log0), dentrykey(ino, str1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, ri0[dentrykey(ino, str1)] ∈ fs0, inodekey(ino) ∈ ri0, inodekey(m) ∈ ri0, ri0[dentrykey(m, str)] ∈ fs0, inodekey(m8) ∈ ri0, dentrykey(m, str) ∈ ri0, ri0[inodekey(ino)] ∈ fs0, fs0[ri0[inodekey(m8)]].directory → dentrykeys(inodekey(m8), ri0) = ∅, ∀ key. key ∈ links(m8, fs0, ri0) ↔ key ∈ ∅ ++ dentrykey(ino, str1), ¬ fs0[ri0[inodekey(m8)]].directory ∧ ¬ boolvar3 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar3 ∧ m4 = fs0[ri0[inodekey(m8)]].size, m9 ≠ 0 ∨ ino = ROOT_INO, m10 ≠ 0 ∨ m = ROOT_INO, ¬ fs0[ri0[inodekey(m8)]].directory ∧ ¬ boolvar1 ∨ fs0[ri0[inodekey(m8)]].directory ∧ boolvar1 ∧ m7 = fs0[ri0[inodekey(m8)]].size ⊦ adr1 = adr2, adr1 = adr3, adr1 = adr4, adr1 = adr5, adr2 = adr3, adr2 = adr4, adr2 = adr5, adr3 = adr4, adr3 = adr5, adr4 = adr5, dentrykey(m, str) = dentrykey(ino, str1), ino = m, ino = 0, m = 0, m8 = ROOT_INO, m8 = 0, adr4 ∈ (ri0 -- dentrykey(m, str))[dentrykey(ino, str1), adr2][inodekey(m), adr3], adr2 ∈ ri0 -- dentrykey(m, str), adr5 ∈ fs0, adr4 ∈ fs0, adr3 ∈ fs0, adr2 ∈ fs0, adr1 ∈ fs0, inodekey(m) ∈ ro, inodekey(ino) ∈ ro, adr3 ∈ (ri0 -- dentrykey(m, str))[dentrykey(ino, str1), adr2], adr5 ∈ (ri0 -- dentrykey(m, str))[dentrykey(ino, str1), adr2][inodekey(m), adr3][inodekey(ino), adr4], inodekey(m8) ∈ ro

Rule argument

spec: set-basic, inst: node-index name: Extension seq: ⊦ ks = ks0 ↔ (∀ key. key ∈ ks ↔ key ∈ ks0) subst: [ks0, ks] → [∅ ++ dentrykey(ino, str1), links(m8, fs0, ri0)] flags: <all paths>

Additional information

Used terms: ∅ ++ dentrykey(ino, str1), links(m8, fs0, ri0)